But bi-directional models neglect the prevalence of asymmetric social relationships in the real world [1]}.
For example, in an empirical network of inter-family relationships in San Juan Sur, a village in Costa Rica, almost two-thirds of the social ties are unidirectional: one family frequency visits another family, while the later family never reciprocates with a return visit [2]}. And
in the empirical friendship network of an Australian National University campus, more than a half of the relationships are unidirectional: one student regards another as her friend, but not conversely [3]}. In the network of Twitter followers (based on a snowball sample crawl across “quality” users in 2009), more than 99% of follower relationships are strictly unidirectional [4]}.
Other examples include email networks [5]}, trust and advice consulting networks [6]}, and social donations [7]} — which all exhibit a high proportion of uni-directional social interactions.
Asymmetric interactions are also widespread outside of the human social domain, in systems ranging from international trade (trade volumes between countries [1]}) to rivers and stream flow (movement of microorganisms, nutrients and organic matters [9]}, [10]}, [11]}).
